Probability and Statistics Pre-course Survey

Purpose The purpose of this survey is to indicate what you already know and think about probability and statistics.

Take your time The questions require you to read and think carefully about various situations. If you are unsure of what you are being asked to do, please raise you hand for assistance.

Part I

On the first few pages are a series of statements concerning beliefs or attitudes about probability, statistics and mathematics. Following each statement is an "agreement" scale which ranges from 1 to 5, as shown below.

1. I often use statistical information in forming my opinions or making decisions.

1 2 3 4 5

2. To be an intelligent consumer, it is necessary to know something about statistics.

1 2 3 4 5

3. Because it is easy to lie with statistics, I don't trust them at all.

1 2 3 4 5

4. Understanding probability and statistics is becoming increasingly important in our
society, and may become as essential as being able to add and subtract.

1 2 3 4 5

5. Given the chance, I would like to learn more about probability and statistics.

1 2 3 4 5

6. You must be good at mathematics to understand basic statistical concepts.

1 2 3 4 5

7. When buying a new car, asking a few friends about problems they have had with their cars is preferable to consulting an owner satisfaction survey in a consumer magazine.

1 2 3 4 5

8. Statements about probability (such as what the odds are of winning a lottery) seem very clear to me.

1 2 3 4 5

9. I can understand almost all of the statistical terms that I encounter in newspapers or on television.

1 2 3 4 5

10. I could easily explain how an opinion poll works.

1 2 3 4 5

1. A small object was weighed on the same scale separately by nine students in a science class. The weights (in grams) recorded by each student are shown below.

6.2 6.0 6.0 15.3 6.1 6.3 6.2 6.15 6.2

The students want to determine as accurately as they can the actual weight of this object. Of the following methods, which would you recommend they use?

_____ a. Use the most common number, which is 6.2.

_____ b. Use the 6.15 since it is the most accurate weighing.

_____ c. Add up the 9 numbers and divide by 9.

_____ d. Throw out the 15.3, add up the other 8 numbers and divide by 8.

2. A marketing research company was asked to determine how much money teenagers (ages 13 - 19) spend on recorded music (cassette tapes, CDs and records). The company randomly selected 80 malls located around the country. A field researcher stood in a central location in the mall and asked passers-by who appeared to be the appropriate age to fill out a questionnaire. A total of 2,050 questionnaires were completed by teenagers. On the basis of this survey, the research company reported that the average teenager in this country spends $155 each year on recorded music.

Listed below are several statements concerning this survey. Place a check by every statement that you agree with.

_____ a. The average is based on teenagers' estimates of what they spend and therefore could be quite different from what teenagers actually spend.

_____ b. They should have done the survey at more than 80 malls if they wanted an average based on teenagers throughout the country.

_____ c. The sample of 2,050 teenagers is too small to permit drawing conclusions about the entire country.

_____ d. They should have asked teenagers coming out of music stores.

_____ e. The average could be a poor estimate of the spending of all teenagers given that teenagers were not randomly chosen to fill out the questionnaire.

_____ f. The average could be a poor estimate of the spending of all teenagers given that only teenagers in malls were sampled.

_____ g. Calculating an average in this case is inappropriate since there is a lot of variation in how much teenagers spend.

_____ h. I don't agree with any of these statements.

3. Which of the following sequences is most likely to result from flipping a fair coin 5 times?

_____ a. H H H T T

_____ b. T H H T H

_____ c. T H T T T

_____ d. H T H T H

_____ e. All four sequences are equally likely

4. Select the alternative below that is the best explanation for the answer you gave for the item above.

_____ a. Since the coin is fair, you ought to get roughly equal numbers of heads and tails.

_____ b. Since coin flipping is random, the coin ought to alternate frequently between landing heads and tails.

_____ c. Any of the sequences could occur.

_____ d. If you repeatedly flipped a coin five times, each of these sequences would occur about as often as any other sequence.

_____ e. If you get a couple of heads in a row, the probability of a tails on the next flip increases.

_____ f. Every sequence of five flips has exactly the same probability of occurring.

5. Listed below are the same sequences of Hs and Ts that were listed in Item 3. Which of the sequences is least likely to result from flipping a fair coin 5 times?

_____ a. H H H T T

_____ b. T H H T H

_____ c. T H T T T

_____ d. H T H T H

_____ e. All four sequences are equally unlikely

6. The Caldwells want to buy a new car, and they have narrowed their choices to a Buick or a Oldsmobile. They first consulted an issue of Consumer Reports, which compared rates of repairs for various cars. Records of repairs done on 400 cars of each type showed somewhat fewer mechanical problems with the Buick than with the Oldsmobile.

The Caldwells then talked to three friends, two Oldsmobile owners, and one former Buick owner. Both Oldsmobile owners reported having a few mechanical problems, but nothing major. The Buick owner, however, exploded when asked how he like his car:
First, the fuel injection went out - $250 bucks. Next, I started having trouble with the rear end and had to replace it. I finally decided to sell it after the transmission went. I'd never buy another Buick.

The Caldwells want to buy the car that is less likely to require major repair work. Given what they currently know, which car would you recommend that they buy?

_____ a. I would recommend that they buy the Oldsmobile, primarily because of all the trouble their friend had with his Buick. Since they haven't heard similar horror stories about the Oldsmobile, they should go with it.

_____ b. I would recommend that they buy the Buick in spite of their friend's bad experience. That is just one case, while the information reported in Consumer Reports is based on many cases. And according to that data, the Buick is somewhat less likely to require repairs.

_____ c. I would tell them that it didn't matter which car they bought. Even though one of the models might be more likely than the other to require repairs, they could still, just by chance, get stuck with a particular car that would need a lot of repairs. They may as well toss a coin to decide.

7. Half of all newborns are girls and half are boys. Hospital A records an average of 50 births a day. Hospital B records an average of 10 births a day. On a particular day, which hospital is more likely to record 80% or more female births?

_____ a. Hospital A (with 50 births a day)

_____ b. Hospital B (with 10 births a day)

_____ c. The two hospitals are equally likely to record such an event.

8. "Megabucks" is a weekly lottery played in many states. The numbers 1 through 36 are placed into a container. Six numbers are randomly drawn out, without replacement. In order to win, a player must correctly predict all 6 numbers. The drawing is conducted once a week, each time beginning with the numbers 1 through 36.

The following question about the lottery appeared in The New York Times (May 22, 1990).

Are your odds of winning the lottery better if you play the same numbers week after week or if you change the numbers every week?

What do you think?

a. I think the odds are better if you play the same numbers week after week.

b. I think the odds are better if you change the numbers every week.

c. I think the odds are the same for each strategy.

9. For one month, 500 elementary students kept a daily record of the hours they spent watching television. The average number of hours per week spent watching television was 28. The researchers conducting the study also obtained report cards for each of the students. They found that the students who did well in school spent less time watching television than those students who did poorly.
Listed below are several possible statements concerning the results of this research. Place a check by every statement that you agree with.

_____ a. The sample of 500 is too small to permit drawing conclusions.

_____ b. If a student decreased the amount of time spent watching television, his or her performance in school would improve.

_____ c. Even though students who did well watched less television, this doesn't necessarily mean that watching television hurts school performance.

_____ d. One month is not a long enough period of time to estimate how many hours the students really spend watching television.

_____ e. The research demonstrates that watching television causes poorer performance in school.

_____ f. I don't agree with any of these statements.

10. Twenty college students participated in a study of the effect of sleep on test scores. Ten of the students volunteered to stay up all night studying the night before the test (no-sleep group). The other 10 students (the control group) went to bed by 11:00 p.m. on the evening before the test. The test scores for each group are shown in the graphs below. Each x represents a particular student's score. For example, the two xs above the 80 in the bottom graph indicate that two students in the sleep group scored 80 on the test.
Examine the two graphs carefully. Then choose from the 6 possible conclusions listed below the one you most agree with.

_____ a. The no-sleep group did better because none of these students scored below 40 and the highest score was achieved by a student in this group.

_____ b. The no-sleep group did better because its average appears to be a little higher than the average of the sleep group.

_____ c. There is no difference between the two groups because there is considerable overlap in the scores of the two groups.

_____ d. There is no difference between the two groups because the difference between their averages is small compared to the amount of variation in the scores.

_____ e. The sleep group did better because more students in this group scored 80 or above.

_____ f. The sleep group did better because its average appears to be a little higher than the average of the no-sleep group.

11. An experiment is conducted to test the efficacy of a new drug on curing a disease. The experiment is designed so that the number of patients who are cured using the new drug is compared to the number of patients who are cured using the current treatment. The percentage of patients who are cured using the current treatment is 50% and 65% are cured who have used the new drug. A p-value of 5% (.05) is given as an indication of the statistical significance of these results. The p-value tells you:

______a. There is a 5% chance that the new drug is more effective than the current treatment.

_____b. If the current treatement and the new drug were equally effective, then 5% of the times we conducted the experiment we would observe a difference as big or bigger than the 15% we observed here.

_____c. There is a 5% chance that the new drug is at least better than the current treatment by at least 15%.

12. Gallup reports the results of a poll that shows that 58% of a random sample of adult Americans approve of President Clinton's performance as president. The report says that the margin of error is 3%. What does this margin of error mean?

______a. One can be 95% "confident" that between 55% and 61% of all adult Americans approve of the President's performance.

______b. One can be sure that between 55% and 61% of all adult Americans approve of the President's performance.

______c. The sample percentage of 58% could be off by 3% in either direction due to inaccuracies in the survey process.

______d. There is a 3% chance that the percentage of 58 is an inaccurate estimate of the population of all Americans who approve of President Clinton's performance as president.